What is Options Theta? Definition, Formula, and Example
Options theta (Θ) is the daily dollar amount an option loses in value from time decay alone, expressed as a negative number for long options and a positive number for short options.
What is Options Theta?
Options theta (Θ) measures how much an option's price decreases each day as expiration approaches, with all other variables held constant. If an option has a theta of −0.07, it loses $7 in value per contract per calendar day from time decay alone. Theta is always negative for long options — you are on the wrong side of time — and always positive for short options, where time decay is your income. Theta is not linear: it accelerates sharply inside the final 30 days before expiration, and it is highest for at-the-money options.
How Theta is Calculated
Theta is the partial derivative of the option's price with respect to time. In the Black-Scholes model for a call:
Θ = −[S · N′(d₁) · σ / (2√T)] − r · K · e^(−rT) · N(d₂)
Where S = stock price, K = strike, σ = implied volatility, T = time to expiration in years, r = risk-free rate, N′(d₁) = standard normal PDF at d₁.
In practice, traders read theta directly from any options chain. It is quoted per share per day, so a theta of −0.08 means −$8 per contract (100 shares) per day. The decay curve is exponential — an option with 60 DTE loses much less per day than the same option with 7 DTE, because the remaining time value is compressed into fewer sessions.
Worked Example: AAPL
AAPL trading at $195. The at-the-money $195 call expiring in 30 days is priced at $5.60 with Θ = −0.09.
| Days to Expiration | Approximate Option Value (AAPL flat) |
|---|---|
| 30 DTE | $5.60 |
| 20 DTE | $4.70 |
| 10 DTE | $3.50 |
| 5 DTE | $2.25 |
| 1 DTE | $0.60 |
| Expiration | $0.00 (AAPL = $195) |
At 7 DTE, the same strike's theta accelerates to approximately −0.18 — double the early-term burn rate — because the remaining $2–3 of time premium must evaporate in 7 sessions instead of 30. Buyers who hold through this zone absorb that accelerating cost; sellers collect it.
When Traders Use Theta
Options sellers — covered call writers, put sellers, iron condor traders — position for theta income. Selling options with 30–45 DTE captures the steepest part of the decay curve without excessive gamma risk. The target is to close at 50% of max profit (theta has done its job) before the trade enters its volatile final week. Options buyers must respect theta's cost: buying a 30-DTE ATM call and holding without movement is a losing proposition even if the stock goes nowhere. Buyers compensate by buying in-the-money (lower theta relative to intrinsic value) or trading near catalysts (earnings, FDA decisions) where a fast directional move can overcome decay.
Limitations and Misconceptions
Theta assumes implied volatility is constant. A large IV expansion — earnings beat, macro shock, short squeeze — can increase an option's price faster than theta erodes it. Long option buyers in pre-earnings setups can be profitable on theta despite holding a position with negative theta. Additionally, theta is highest for ATM options, but ATM options also carry the most gamma exposure — the elevated theta is compensation for that directional risk, not free income. Selling high-theta weekly options appears profitable in backtests but carries outsized gap risk from unexpected binary events that don't appear in normal distributions.